Macro-velocity Model Research Articles

Velocity model building via combining seismic slope tomography and supervised deep learning

AbstractSeismic slope tomography is an effective method to build macro velocity model. In order to improve the accuracy and resolution of the slope tomography, we proposed a novel approach that combines slope tomography with supervised deep learning. First, the slope tomography is used to obtain the macro velocity model and the positions of reflection points. Subsequently, the slope tomographic model, positions of reflection points and the corresponding observed traveltimes are used as inputs simultaneously for a neural network, whereas the actual velocity models are used as the labels. Through training the neural network with sufficient samples, the mapping from the inputs to the real velocity model is established. The neural network learns the background velocity of the real model from the smooth tomographic model, the velocity details from the traveltimes and the formation interface information from the positions of reflection points. Consequently, a high‐accuracy and high‐resolution velocity model is obtained on the basis of the slope tomographic model. Both tests on synthetic seismic data and applications to field seismic data demonstrate the effectiveness of the proposed method.

Internal-multiple-elimination with application to migration using two-way wave equation depth-extrapolation scheme

Internal multiple interference, affecting both seismic data processing and interpretation, has been observed for long time. Although great progress has been achieved in developing a variety of internal-multiple-elimination (IME) methods, how to increase accuracy and reduce cost of IME still poses a significant challenge. A new method is proposed to effectively and efficiently eliminate internal multiples, along with its application in internal-multiple-eliminated-migration (IMEM), addressing this issue. This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation, which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously, and complete internal-multiple-elimination processing, adaptively and efficiently. The proposed method has several features: (1) input data is same as that for conventional migration: source signature (used for migration only), macro velocity model, and receiver data, without additional requirements for source/receiver sampling; (2) method is efficient, without need of iterative calculations (which are typically needed for most of IME algorithms); and (3) method is cost effective: IME is completed in the same depth-extrapolation scheme of IMEM, without need of a separate processing and additional cost. Several synthesized data models are used to test the proposed method: one-dimensional model, horizontal layered model, multi-layer model with one curved layer, and SEG/EAGE Salt model. Additionally, we perform a sensitivity analysis of velocity using smoothed models. This analysis reveals that although the accuracy of velocity measurements impacts our proposed method, it significantly reduces internal multiple false imaging compared to traditional RTM techniques. When applied to actual seismic data from a carbonate reservoir zone, our method demonstrates superior clarity in imaging results, even in the presence of high-velocity carbonate formations, outperforming conventional migration methods in deep strata.

Robust and efficient waveform-based velocity model building by optimal transport in the pseudotime domain: An ocean-bottom cable case study in the North Sea

Full-waveform inversion (FWI) in the North Sea has demonstrated its imaging power starting from low-resolution models obtained by traveltime tomography, enriching them with geologically interpretable fine-scale details. However, building a traveltime-based kinematically accurate starting model for FWI is a time-consuming and rather subjective process requiring phase identification and selection. The two main problems faced by FWI starting from noninformative initial models are the susceptibility to cycle skipping and a lack of sensitivity to low wavenumbers in the deep subsurface not sampled by turning waves. On a North Sea ocean-bottom cable 3D data set, a novel [Formula: see text] building methodology is applied that addresses those issues by jointly inverting reflections and refractions (joint full-waveform inversion [JFWI]) using a robust misfit function in the vertical traveltime domain (pseudotime). Pseudotime addresses reflectivity-velocity coupling and attenuates phase ambiguities at short offsets, whereas a graph-space optimal transport (GSOT) objective function with dedicated data windowing averts cycle skipping at intermediate-to-long offsets. A fast and balanced reflectivity reconstrution is obtained prior to JFWI thanks to an asymptotic-preconditioned impedance waveform inversion ([Formula: see text]WI). Starting from a linearly increasing one-dimensional model, GSOT-pseudotime JFWI is effective at obtaining a meaningful P-wave velocity macromodel down to depths sampled by reflections only, without phase identification and picking. P-wave FWI, starting from the JFWI-based model, injects the high wavenumbers missing in the JFWI solution, attaining apparent improvements in shallow and deep model reconstruction and imaging compared with the previous studies in the literature, and a satisfactory prediction of the ground-truth logs.

Monochromatic wave equation reflection traveltime inversion

Wave equation reflection traveltime inversion (WRTI) is a fundamental method for interrogating the deep subsurface macrovelocity model. The time-domain WRTI calculates the gradient through the crosscorrelation of the source background and receiver scattered wavefields and the crosscorrelation of the source scattered and receiver background wavefields. During the backward propagation of the adjoint source, access to the source background and scattered snapshots of the entire propagation time is required. Because the source and receiver wavefields are extrapolated in opposite temporal directions, these source background and scattered wavefields are either stored in memory or reconstructed by additional wavefield extrapolation. This leads to a heavy memory burden and/or high computational cost. To address these challenges, we develop a new frequency-domain WRTI that is based on a monofrequency. By using the wavenumber coverage and gradient analyses, we prove that the monochromatic WRTI can produce comparable wavenumbers with time-domain and multifrequency-based WRTI. Our method directly stores monochromatic wavefields in memory because only one frequency is used for the gradient calculation. Therefore, our method significantly outperforms the conventional time-domain implementation in terms of memory requirement and computational cost. The accuracy of the monochromatic WRTI method is validated by gradient and result comparisons of several models with different complexities. Finally, we determine the effectiveness of our method by applying it to offshore streamer data.

Seismic differential semblance-oriented migration velocity analysis — Status and the way forward

Differential semblance optimization (DSO) is a seismic waveform inversion approach. It has been developed to remove the limitation of conventional full-waveform inversion as a velocity model building tool when only reflected waves are available. It has connections with migration velocity analysis (MVA) techniques defined in the image domain to build macrovelocity models, with a split between the macromodel and the small-scale heterogeneities. Among the various DSO approaches, DSO-MVA has unique characteristics for velocity model building of complex structures, while ensuring the convergence to the global minimum in a local optimization approach: the wavefields are computed with the two-way wave equation operators, focusing panels are built in a survey-sinking mode, and the quality of the macrovelocity model is evaluated on common-image gathers in the subsurface-offset domain through a differential annihilator. We review the significant aspects that have been better understood over the past 15 years and discuss the way forward. The first identified issue has been the imprint of the small-scale heterogeneities on the macromodel update that is revealed with the use of wave equation-based Green’s functions and an ad hoc solution is subsequently developed by slightly modifying the definition of the objective function. A second important aspect has been the development of efficient approaches to compute the required quantitative migration based on approximate inverses to replace the previously used migrations. The issue of correctly interpreting the amplitudes has also moved into one of an improved model parameterization, i.e., from constant-density acoustics media to full acoustic media as a path toward fully viscoelastic media. Finally, we discuss the way forward with the challenges of extending DSO-MVA beyond the single scattering approximation, for processing diving waves and multiples, and also the challenge of numerical implementation, which remains critical even in two dimensions, for applicability to large-scale real data.

Finite-frequency sensitivity kernels and hierarchical traveltime and waveform inversion of direct and reflected waves from vertical seismic profile data

Wave-equation-based traveltime or waveform inversion updates the velocity model along finite-frequency sensitivity kernels and exhibits higher accuracy than ray-based tomography. Owing to special geometry, the kernels for vertical seismic profile (VSP) data are different from those for surface seismic data. We have used the Born approximation to compute the traveltime and waveform kernels for direct and reflected waves from VSP data. Based on the property of sensitivity kernels for different information and arrivals, we develop a hierarchical inversion scheme: joint wave-equation traveltime inversion (JWETI) of direct and reflected waves, joint waveform inversion (JWI) of direct and reflected waves, and full-waveform inversion (FWI) of the reflected wave. The traveltime kernels, the waveform kernels, and the migration isochrones are used to retrieve the long-, intermediate-, and short-wavelength components of the velocity model, respectively. Numerical tests on synthetic and real walkway VSP data reveal that the JWETI stage obtains a plausible velocity macromodel, which can be treated as a starting model for subsequent JWI and FWI stages. The JWI stage is a transition between JWETI and FWI and helps to improve the structures of the deep layers of the model. The FWI stage offers some high-wavenumber contents to the inverted model. For the VSP survey, the transmitted direct waves can be used to reduce the dependence of FWI on the initial model. However, the conventional reflection-based wave-equation traveltime inversion and FWI still suffer from cycle skipping when the initial model is far away from the real model. In contrast, the hierarchical inversion scheme can yield reasonable inversion results around the borehole, even when large velocity errors are present in the starting model.

Seismic imaging of medical ultrasound data: Towards in vivo applications

This study presents the application to medical ultrasonography of a high value-added imaging method developed in the context of geophysical exploration and based on the undulatory description of the physical process. Currently, the most serious limitation of conventional medical ultrasound systems is the implicit assumption of constant-velocity media stemming from the widespread use of geometrical ray-based imaging algorithms and leading to phase aberration phenomena in the case typical of the human body of two or more tissues with different velocities. As a result, imaging of targets underlying tissue layers can be severely degraded. To address this problem, the proposed algorithm is designed expressly for variable-velocity media, providing high-resolution images by implementing the solution of the one-way wave equation. From a macro-velocity model, the illuminated structures are imaged by correlating, in the frequency domain and for each source element, the simulated emitted wavefield with the back-propagated echoes sensed by the ultrasound transducer. The pointwise sum of the correlations reveals, constructively, all diffraction points and reflectors in the image space. The experiments conducted on in vitro laboratory data reveal remarkable spatial resolution and very accurate target positioning, even in the presence of an aberrant layer. A preliminary in vivo test also demonstrates the method's effectiveness in imaging echoes recorded on human tissues, giving a glimpse of its potentiality for clinical purposes.

Robust and efficient waveform-based velocity-model building by optimal transport in the pseudotime domain: Methodology

Full-waveform inversion (FWI) aims at a broadband reconstruction of the subsurface physical properties by fitting the entire recorded wavefield. In realistic exploration seismic surveys, however, conventional FWI often fails to retrieve the deep velocity model due to the limited penetration depth of diving waves. Joint FWI (JFWI) unifies reflection-waveform inversion and early arrival waveform inversion to reconstruct simultaneously the shallow and deep subsurface kinematics. However, several factors limit the appeal of JFWI velocity-model building: (1) conflict between fixed reflectivity and evolving kinematics, creating phase ambiguity at short offsets; (2) susceptibility to cycle skipping at mid-to-long offsets, thus reliance on the quality of the starting model; and (3) cost of building and updating the reflective model. We have developed a fully operational JFWI-based methodology that systematically addresses the aforementioned issues. JFWI is reformulated in the pseudotime domain, to enforce consistency between velocity and reflectivity in a cost-effective fashion, without repeated least-squares migrations. A JFWI graph-space optimal transport (GSOT) objective function is designed to avert cycle skipping, whereas nonuniqueness is mitigated at no extra cost by smoothing the velocity gradient along the structures extracted from the reflective model. A dedicated asymptotic-based preconditioner is developed for impedance waveform inversion, making it possible to obtain sharp and balanced reflective images in a fraction of the time. We determine that pseudotime GSOT-JFWI retrieves complex velocity macromodels from limited-offset data sets with minimal preprocessing, starting from noninformative initial solutions. Compared with depth-domain JFWI, the computing cost is reduced significantly, along with a simpler and less subjective design of data weighting and inversion strategy. Pseudotime GSOT-JFWI provides FWI with the necessary low wavenumbers to converge to the broadband model, reducing the need for accurate starting models, on the road to a fully waveform-based imaging workflow.

Sparse Inversion for the Iterative Marchenko Scheme of Irregularly Sampled Data

The Marchenko method is a data-driven way that makes it possible to calculate Green’s functions from virtual points in the subsurface using the reflection data at the surface and requiring only a macro velocity model. This method requires collocated sources and receivers. However, in practice, irregular sampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green’s functions. To solve this problem, this paper proposes to integrate a sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply the sparse inversion during the iterative process. To reduce the strict requirements on acquisition geometries, our work deals with the situation in which the sources are subsampled where the integrations are carried out over the receivers, while the existing point spread function method solves the situation where the receivers are subsampled. We make a step to handle both situations at the same time by integrating this method with our work because of the same iterative framework. Our new method is applied to a two-dimensional numerical example with irregularly sampled data. The result shows that it can effectively fill gaps in the obtained focusing functions and Green’s functions in the Marchenko method.

An Automatic Velocity Analysis Method for Seismic Data-Containing Multiples

Normal moveout (NMO)-based velocity analysis can provide macro velocity models for prestack data processing and seismic attribute inversion. Datasets with an increasing size require conventional velocity analysis to be transformed to a more automatic mode. The sensitivity to multiple reflections limits the wide application of automatic velocity analysis. Thus, we propose an automatic velocity analysis method for seismic data-containing multiples to overcome the limit of multiple interference. The core idea of the proposed algorithm is to utilize a multi-attribute analysis system to transform the multiple attenuation problem to a multiple identification problem. To solve the identification problem, we introduce the local similarity to attribute the predicted multiples and build a quantitative attribute called multiple similarity. Considering robustness and accuracy, we select two supplementary attributes based on velocity and amplitude difference, i.e., velocity variation with depth and amplitude level. Then we utilize the technique for order preference by similarity to ideal solution (TOPSIS) to balance weights for different attributes in automatic velocity analysis. An RGB system is adopted for multi-attributes fusion in velocity spectra for visualization and quality control. Using both synthetic and field examples to evaluate the effectiveness of the proposed method for data-containing multiples, the results demonstrate the excellent performance in the accuracy of the extracted velocity model.

Wave-equation traveltime slope inversion by combining finite difference and cross-correlation methods

As an essential step in seismic inversion, velocity macromodel building provides a low-wavenumber background velocity model for seismic imaging and full waveform inversion. Defined as the first-order partial derivative of traveltime with regard to spatial coordinates, slope information has been directly or indirectly applied in ray-based geophysical inversion to retrieve models containing low and intermediate wavenumbers. In this study, to use slopes of locally coherent events in background velocity model building, we extend the slope inversion from ray theory to wave equation, which we name wave-equation traveltime slope inversion (WSI). Unlike traditional ray-based slope inversion, which relies on tedious picking of continuous horizons, we compute slope conveniently and robustly through cross-correlation and finite difference methods. Furthermore, we present the formulation of wave-equation traveltime slope inversion under the framework of wave-equation traveltime inversion. Traveltime and slopes are distinct data attributes that play different roles in reconstructing low-wavenumber background velocity models. Compared with the classic traveltime inversion, the wave-equation traveltime slope inversion is more sensitive to local velocity changes. Numerical examples demonstrate that the proposed method improves the horizontal resolution in velocity model building, which especially shows excellent potential in obtaining a higher lateral resolution of reconstruction for steeply dipping structures than traditional wave-equation traveltime inversion. What's more, this study makes the joint inversion of travel time and slope based on the wave equation possible, which can theoretically bring a higher resolution stabilized inversion.

Wave-equation migration velocity analysis via the optimal-transport-based objective function

Wave-equation migration velocity analysis builds a kinematically accurate macrovelocity model containing the large-scale structures of the model for seismic imaging or full-waveform inversion (FWI). Differential semblance optimization formulates the misfit function in the subsurface domain by applying a penalty to the unfocused subsurface-offset gathers or the nonflattened angle gathers. Such a penalty leads to gradients with strong artifacts and spurious oscillations, which then leads to slow convergence. We formulate the misfit function using the optimal transport (OT) among neighboring traces in angle-domain common-image gathers (CIGs). Specifically, we measure the unflatness of the gathers by comparing the Wasserstein distance of adjacent traces. Because CIGs are ideal to form a probability distribution, which is required by OT, it is natural to use OT to measure the time shifts between two distributions. Our objective function exhibits well-behaved convex and unimodal properties in a simple model with a single interface, and it is expected to be minimum for the correct velocity when the angle gathers are flat. A synthetic data set example on the Marmousi model indicates the ability of our method to provide an initial model for FWI that allows FWI to converge. We also apply the approach on a marine field data set to further demonstrate its effectiveness in estimating the macrovelocity model.

On the Retrieval of Forward-Scattered Waveforms From Acoustic Reflection and Transmission Data With the Marchenko Equation.

A Green's function in an acoustic medium can be retrieved from reflection data by solving a multidimensional Marchenko equation. This procedure requires a priori knowledge of the initial focusing function, which can be interpreted as the inverse of a transmitted wavefield as it would propagate through the medium, excluding (multiply) reflected waveforms. In practice, the initial focusing function is often replaced by a time-reversed direct wave, which is computed with help of a macro velocity model. Green's functions that are retrieved under this (direct-wave) approximation typically lack forward-scattered waveforms and their associated multiple reflections. We examine whether this problem can be mitigated by incorporating transmission data. Based on these transmission data, we derive an auxiliary equation for the forward-scattered components of the initial focusing function. We demonstrate that this equation can be solved in an acoustic medium with mass density contrast and constant propagation velocity. By solving the auxiliary and Marchenko equation successively, we can include forward-scattered waveforms in our Green's function estimates, as we demonstrate with a numerical example.

Elimination of free-surface-related multiples by combining Marchenko scheme and seismic interferometry

The removal of free-surface-related multiples plays an important role in seismic data processing. We have developed a novel scheme for predicting free-surface-related multiples by combining the revised Marchenko equations with free-surface effects and convolutional seismic interferometry. This data-driven method can create the free-surface-related multiple prediction using only the reflection response recorded at the free surface and a macrovelocity model estimated in the first layer. By setting only one reference boundary in the first layer, we can stably and efficiently retrieve the one-way upgoing and scattered downgoing Green’s functions at virtual focusing points and then predict all orders of free-surface-related multiples. Numerical experiments on a 2D model and a subset of the Marmousi model indicate that this method can accurately and efficiently predict the traveltimes of all orders of free-surface-related multiples. After applying least-squares matched filtering, all orders of the surface-related multiples can be effectively eliminated from the raw shot gathers.

Joint wave-equation traveltime inversion of diving/direct and reflected waves for P- and S-wave velocity macromodel building

Full-waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We have developed a joint diving/direct and reflected wave WETI (JDRWETI) method to build P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves and PP- and PS-reflections) through the dynamic warping scheme and construct a misfit function using the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP- and PS-reflections. For an explosive source, the kernels of the diving/direct wave and PP-reflections and the kernel of the PS-reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: First, we invert the P- and S-wave velocity models using the P-wave gradients, and then we improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field data sets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.

3-D Virtual Seismology

We create virtual sources and receivers in a 3D subsurface using the previously derived single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at the Earth's surface, a macro velocity model and the Marchenko method. The homogeneous Green's function is a Green's function superposed with its time-reversal. Unlike the classical homogeneous Green's function representation, our approach requires no receivers on an enclosing boundary, however, it does require the source signal to be symmetric in time. We demonstrate that in 3D, the single-sided representation is an improvement over the classical representation by applying the representations to numerical data. We retrieve responses to virtual point sources with an isotropic and with a double-couple radiation pattern and compare the results to a directly modeled reference result. We also demonstrate the application of the single-sided representation for retrieving the response to a virtual rupture that consists of a superposition of double-couple point sources. This is achieved by obtaining the homogeneous Green's function for each source separately, before they are transformed to the causal Green's function, time-shifted and superposed. The single-sided representation is also used to monitor the complete wavefield that is caused by a numerically modeled rupture. However, the source signal of an actual rupture is not symmetric in time and the single-sided represenation can therefore only be used to obtain the causal Green's function. This approach leaves artifacts in the final result, however, these artifacts are limited in space and time.

Velocity Analysis Using Separated Diffractions for Lunar Penetrating Radar Obtained by Yutu-2 Rover

The high-frequency channel of lunar penetrating radar (LPR) onboard Yutu-2 rover successfully collected high quality data on the far side of the Moon, which provide a chance for us to detect the shallow subsurface structures and thickness of lunar regolith. However, traditional methods cannot obtain reliable dielectric permittivity model, especially in the presence of high mix between diffractions and reflections, which is essential for understanding and interpreting the composition of lunar subsurface materials. In this paper, we introduce an effective method to construct a reliable velocity model by separating diffractions from reflections and perform focusing analysis using separated diffractions. We first used the plane-wave destruction method to extract weak-energy diffractions interfered by strong reflections, and the LPR data are separated into two parts: diffractions and reflections. Then, we construct a macro-velocity model of lunar subsurface by focusing analysis on separated diffractions. Both the synthetic ground penetrating radar (GPR) and LPR data shows that the migration results of separated reflections have much clearer subsurface structures, compared with the migration results of un-separated data. Our results produce accurate velocity estimation, which is vital for high-precision migration; additionally, the accurate velocity estimation directly provides solid constraints on the dielectric permittivity at different depth.

An adaptive finite-difference method for accurate simulation of first-arrival traveltimes in heterogeneous media

Accurate simulation of first-arrival traveltimes is the foundation of seismic depth imaging and macro velocity model building for full waveform inversion. In this paper, an adaptive finite-difference method based on Gauss-Seidel iterations has been developed to achieve a more accurate calculation of first-arrival traveltimes in heterogeneous media. The plane wave, spherical wave and refracted wave approximations of local eikonal solver are used to simulate the seismic traveltimes, respectively. Then, a novel updating strategy based on Fermat principle is proposed to make the accurate choice of factor and traveltime, adaptively. The new algorithm can guarantee the high accuracy of traveltime simulation at the grid point not only near the source point, but also at a great distance from the source point. With the combination of global fast sweeping method, the traveltime simulation is unconditionally stable and all possible propagating directions of different seismic waves are considered to describe the complex propagating process due to the velocity model with sharp variations. Several numerical examples were solved to demonstrate that the adaptive finite-difference method can fulfill the accurate, efficient and robust simulation of first-arrival traveltimes.

Target-oriented full-waveform inversion using Marchenko redatumed wavefields

SUMMARY Full-waveform inversion (FWI) has demonstrated increasing success in estimating medium properties, but its computational cost still poses challenges in moving towards high-resolution imaging of targets at depth. Here, we propose a target-oriented FWI method that inverts for the medium parameters confined within an arbitrary region of interest. Our method is novel in terms of both local wavefield modelling and data redatuming, in order to build a target-oriented objective function which is sensitive to the target medium only without further assumptions about the medium outside. Based on the convolution-type representation theorem, our local forward modelling operator propagates wavefields within the target medium only while providing full acoustic coupling between the target medium and the surrounding geology. A key requirement of our local FWI method is that the subsurface wavefields surrounding and inside the target be as accurate as possible. As such, the subsurface wavefields are retrieved by the Marchenko method, which can redatum the single-sided surface reflection data to the target zone while preserving both primary and multiple reflections, with minimal a priori knowledge of the full-domain medium. Given a sufficiently accurate initial velocity macromodel, our numerical examples show that our local FWI method resolves the reservoir zone of a 2-D Barrett Unconventional P-wave velocity model much more efficiently than the conventional full-domain FWI without significantly sacrificing accuracy. Our method may further enable FWI approaches to high-resolution imaging of subsurface targets.

Accelerating 2D frequency-domain full-waveform inversion via fast wave modeling using a model reduction technique

Full-waveform inversion (FWI) is widely used to infer earth structures and rock properties. In FWI, most of the computation arises from the repeated simulations of wave propagation. Although frequency-domain implementations have several advantages, solving the Helmholtz equation incurs a major computational cost associated with the inversion of large matrices. Hence, we have used a new model reduction technique called the generalized multiscale finite-element method (GM FEM) to perform this task rapidly for forward and backward simulations. This in turn leads to the acceleration of the FWI. In addition, the multiscale finite-element approach allows flexible, adaptive selection of modeling parameters (i.e., grid size, number of basis functions) for different target frequencies, providing further speed up. We apply this frequency-domain, multiscale FEM approach to the Marmousi-2 model, and the FWI results indicated how varying the number of basis functions can control the trade-off between the accuracy and computational speed. In addition, we introduced FWI examples applied to field data from the Gulf of Mexico. These field data examples indicate that applying our multiscale FWI with a relatively small number of basis functions can quickly construct a macrovelocity model using low frequencies. We also evaluate a strategy to optimize the FWI procedure by using frequency-adaptive multiscale basis functions based on the target frequency group. In general, we can reduce the run time by up to 30% through the application of GM FEM wave modeling in FWI.